The repeal or weakening of motorcycle helmet use laws in thirty-one states between 1976 and 1983 has generated a vigorous debate over the effectiveness of helmets in the prevention of fatalities and the reduction of injury severities. Statistical studies that have explored these issues have suffered from the lack of an accurate and detailed data set and, more importantly, have neglected to integrate causal models into their analysis. While the former problem has been alleviated by the extensive data collection techniques employed by Hurt, et al. (1981a), the latter problem has not been addressed. The statistical techniques employed fail to control for the multifacted and interrelated factors involved in motorcycle fatalities and injuries and thus conflate the effects of such factors and erroneously assign them to helmet use.

The purpose of this paper is to develop, estimate, and statistically test three causal models for: (1) the probability of a fatality; (2) the severity of head injuries; and (3) the severity of neck injuries, where each dependent variable is conditional on the occurrence of a motorcycle accident. A latent variable framework is employed in each case and particular attention is paid to the effectiveness of helmets in each instance.

In contrast to previous findings, it is concluded that: (1) motorcycle helmets have no statistically significant effect on the probability of fatality; and (2) past a critical impact-speed' measured by the normal component of velocity to the helmet, helmets increase the severity of neck injuries. It is also shown that helmets reduce the severity of head injuries. Thus, an individual or legislator is faced with a tradeoff between head and neck injuries in deciding whether or not to wear or mandate helmet use. Further analysis reveals that all possible combinations of the intensity-of the tradeoff, defined in terms of the severity of head injuries forgone and the severity of neck injuries incurred from helmet usage, are equally likely.

The arguments in this paper are presented in five remaining sections. Section II presents an overview of existing statistical studies. The next section develops the basic model and its variants. Section IV discusses the data. Section V presents our results. Finally, Section VI contains our conclusions and their policy implications.

II. Overview

Existing statistical research on helmet effectiveness employs two alternative methodologies to analyze accident data. These techniques test the difference-between death rates. injury rates, location rates of injuries, and severity rates of particular types of injuries. These rates are compared either for a similar period of time before and after helmet law repeal or for helmeted riders and non-helmeted riders during a single time period subsequent to helmet law repeal.1 In each case statistically significant differences are attributed to helmet use or non-use. Typical results associated with this literature are death and injury rates two to three times greater for non-helmeted riders and increases in occurrence rates in repeal years that range from 19% to 63%.

The major limitation of previous studies is the lack of an effective control for other factors that concurrently determine death and injury rates. On one hand, helmet-non-helmet comparisons fail to consider differences in these two categories of riders. The most plausible hypothesis is that helmeted riders are more risk- averse and thus: (1) have lower pre-crash and thus crash speeds; (2) are less likely to be involved in accidents; (3) and are less likely to combine alcohol consumption and driving.2 Such behavior rather than helmet use per se may dramatically reduce the probability of a fatality or the severity of an injury.

On the other hand, before and after designs fail to control for dramatic trends in the data. In particular trends towards: (1) lower median age of motorcycle owners; (2) higher average annual miles traveled; (3) lower average experience levels of riders: and (4) higher displacement machines, are not considered.3 Given the relationships between engine displacement and potential speed, age and risk-aversion, and risk-aversion, crash speeds, and alcohol ingestion, simple before-after comparisons cannot be expected to isolate the effectiveness of helmet use.

In the next section we develop an econometric model that considers the determinants of the probability of death, and the severity of head and neck injuries. This approach allows us to isolate the individual effect of helmet use on the variables in question.

III. The Econometric Model

Variations of one basic model are employed for each of the three dependent variables considered. The classification of explanatory variables into three broad groups facilitates the development of the model. This typology consists of: (1) factors governed by the laws of physics; (2) physiological factors; and (3) human factors and operator characteristics. We consider each of these categories in order.

An informative method for understanding motorcycle trauma is to consider it as the result of uncontrolled mechanical energy transfer.4 Motorcycle accidents result in serious injuries because of the speeds involved and the associated energy that the laws of physics tell us must be dissipated in the crash. In this light, the input energy and circumstances surrounding the dissipation of that energy are the crucial physical factors associated with injury severity.

Besides a measure of the energy transferred to the motorcycle operator--the potential for bodily damage--such factors as the compressibility or deformability of the impacted object, employment of a helmet as an energy handling device and the engineering and design limitations of such devices must be considered. The compressibility of an impacted object determines the amount of kinetic energy utilized to deform that object and thus not available to injure the rider. Helmets, in turn, control or mediate within bounds the transfer of impact energy to the head. The current engineering design, safety standards, and production techniques applicable to motorcycle helmets place limits on the energy dissipating capacity of these protective devices.5 If sufficient energy is involved to overcome these capabilities, damage to the head and possibly the neck may occur. This implies that the effectiveness of the helmet is mediated by the force applied to the helmet.

As a measure of input energy, we employ two variants of the kinetic energy of the motorcycle operator that results from a collision. The formula for kinetic energy can be expressed as K=1/2mv2, where m is the mass of the operator and v is the velocity assumed by that mass. Given the availability of data, two variants of the velocity variable are used. These variables are first approximations of v based on physical laws. The first measure (K1) is simply the crash speed of the motorcycle. In the alternative specification (K2), v is assigned either the relative impact velocity of the motorcycle and other crash-involved vehicle, or the motorcycle crash speed.6 The former is assigned when the injury mechanism associated with the rider's most severe injury is the other vehicle, while the latter is employed in all other circumstances.7 It is assumed that the dependent variable is positively related to K1 and K2.

The effect of helmets is modeled through two variables: a qualitative variable, HI, that distinguishes between helmet use and non-use and an interaction term, HI, constructed from the product of H and the normal component of impact velocity to the helmet. This specification implies that the overall effectiveness of the helmet decreases with impact speed. Helmet engineering considerations lead us to expect a negative coefficient for HI and a positive coefficient for H.

Finally, a compressibility variable is not included in our final specification. The results from estimated equations that include such a variable, not reported, find the coefficient to be insignificant in all cases.8 Deletion of this variable from the appropriate equations results in changes in the coefficients and standard errors of all other variables that are negligible.

The physiological factors considered are the effect of age and alcohol consumption. Individuals can be considered to have an "injury threshold" which is based on physiological parameters. Those parameters in turn depend on an individual's age in such a manner that older people have a reduced resistance to injury.9 Alcohol ingestion affects the severity of injuries in two ways. First, the presence of alcohol hinders not only the clinical diagnosis of injuries but the self-detection of injuries.l0 More importantly, the cardiovascular effects of alcohol significantly inhibit the process of homeostasis, especially the dynamic management of circulatory stability.ll These two physiological variables are respectively denoted by A and BA and the expected signs of their coefficients are positive.

Other physiological factors considered but not included in the final equations include drug involvement, and permanent physiological impairment. The estimated coefficients of these variables were statistically insignificant in all cases and deletion of these variables from the equations resulted in negligible changes in the remaining coefficients and their standard errors.

While many human factors and operator characteristics were analyzed, the final equations include only two: the amount of rider on-road experience, EX , and a binary variable, EA, which establishes whether or not (EA = 1, or EA =0) the rider had taken the correct evasive action for the particular accident situation. A special case of a linear spline, one where the slope of the linear segment beyond a critical experience level is constrained to be zero is used to model the experience variable. This implies that EX = EX for 0 < EX < EX* and EX = EX* otherwise, where EX* is the critical experience level. This specification is theoretically justified by marginal returns from additional experience which approach zero past some critical experience level, but is also necessitated by the nature of the data (discussed below). The expected signs for the EX and EA coefficients are negative.

Other factors considered include driver training, the operator's past accident and violation history, the height and weight of the operator, and whether or not the rider voluntarily separated from the motorcycle before impact. In all cases and in all equations the coefficients of these variables were statistically insignificant and their deletion did not alter in any significant way the remaining coefficients or standard errors.

Finally, in order to control for any influences of risk aversion not captured by K1, K2, BA. or H and thus to avoid specification bias, proxy variables such as income, number of children, marital status, and education were included in our equations. These variables were singularly and in all possible combinations statistically insignificant and were eliminated from the equations with the same results as other such variables. Also considered and eliminated in similar fashion were measures of traffic density and a coefficient of braking friction.

The major limitation of our specification is the exclusion, due to data limitations, of a variable that captures the quality and expeditious delivery of medical services. While the problem of specification bias is unlikely, the statistical and quantitative importance of such a variable cannot be established.

A. Fatality Model

In order to model the probability of a fatality, we define a dichotomous variable, Di, where Di = 1 if the operator died given that an accident occurred and Di = 0 otherwise. We also specify a latent variable Di an individual's propensity to die conditional on the occurrence of an accident. For notational simplicity and ease of exposition, we drop all references in the remainder of the text to the conditional nature of the three dependent and latent variables. We assume that

where Xi is a vector of independent variables, ß is a vector of unknown parameters, and E is a random error term. It is assumed that Ei are i.i.d. drawings from In this model Xi includes K in one of its two forms. H, HI, A, BA, EA, EX and a constant term. Di can now be defined in terms of in the following manner:

where Z* is a threshold beyond which an individual expires. Given this specification the probe ability that Di = 1 can be expressed as

where F is the standard normal distribution function. The maximum likelihood (ML) probit estimates for the parameters of this model are reported in section V.A. below.

B. Head Injury Severity (HIS) Model

In this model the dependent variable, HS, is the sum of squared severities for all head injuries sustained by the driver, where the severity of each injury is measured by the Abbreviated Injury Scale (AIS).12 Although -the dependent variable is continuous, the large number of limit observations,13 suggest a Tobit specification. We define a latent variable, , the sum of squared severities for all head injuries, and assume that

where ß, Xi, and Ei are as defined in the fatality model. HSi can now be defined in terms of HSi in the following fashion

Given this specification the regression function can be written as

where f is the density function of the standard normal variable. The ML Tobit estimates for the parameters of this model are reported below.

C. Neck Injury Severity (NIS) Model

The dependent variable in this case is NS, the sum of squared severities for all neck injuries.14 Given the large number of limit observations, a Tobit specification is utilized.l5 Let be the sum of squared severities from all neck injuries and assume that

where ß and Ei are defined as in the previous models. One additional explanatory variable (HW) is included in Xi. This variable is an interaction variable and is formed as the product of H and the weight of the helmet.

The inclusion of both the HI and HW interaction variables in the neck equation are justified by the laws of physics. Impacts to the helmet are capable of causing a flexure or extension displacement (cervical stretch) of the neck and the prospect of a related neck injury. While a helmet may attenuate head impact and thus the extension-flexsion response of the neck, this result can only be expected to occur until some critical impact speed beyond which the energy absorbing capabilities of the helmet are surpassed. Beyond that speed, the added mass of the helmet increases the inertial and post-impact response of the neck and is theoretically related to the severity of neck injuries.16

Expressing NSi in terms of we obtain:

Given this specification the regression function can be written as

The ML Tobit estimates for the parameters of the model when HWi is both included and excluded from Xi are reported below.

IV. The Data

The data used was collected from the on-scene in-depth investigations of 900 motorcycle accidents, in the Los Angeles area, supervised by Hurt et al. (1981a). Each accident was completely reconstructed and 1,045 data elements covering accident characteristics, environmental factors, vehicle factors, motorcycle rider, passenger, and other vehicle driver characteristics, and human factors including both injuries and protection system effectiveness were recorded. The data was collected by a multi-disciplinary research team which insured more accurate and detailed information than is typically available from police and hospital records.17

A subsample of 644 cases was selected based on our twofold treatment of missing data. In general, cases with missing data on the independent variables were dropped from the sample. In the case where such a deletion would result in possible selection bias or the significant loss of data, missing values were assigned the mean value of the variable in question.18

As argued above, one limitation of the data directly affects the specification of our model. While the use of a linear spline to model the effects of EX is theoretically justified, it is also necessitated by the truncated range used to record that variable: values of EX > 96 months were assigned a value of 97. While different critical values of EX < 96 were used, the best fit, occurred when EX* = 96. While it was not possible to test critical points above 96 to determine if a better fit existed, the EX variable was insignificant in all but the HIS model. And deletion of this variable in other models had negligible influence on all results.

The definition, construction, units of measurement, and sample means for all variables in our final equations are contained in Appendix A.

V. Results

The results of the fatality model and the HIS and NIS models are respectively reported in Tables I, III, and IV. Estimates are based on the 644 cases remaining after the treatment of the missing values. For each model two equations corresponding to the two variants of K are reported. In the NIS model an additional two equations associated with the inclusion-exclusion of the HW variable are reported.

A. Fatality Model

The results in Table I reveal that the coefficients of all variables take on their expected signs. Both the H and HI variables are insignificant, indicating that:

Helmet use has no statistically significant effect on the probability of death.

The major determinants of the probability of a fatality are the kinetic energy imparted to the rider--the potential for bodily damage--and the operator's blood alcohol level. The results also reveal that the proper execution of evasive action, an individual's age, and experience level have no statistically significant impact on the probability of a fatality. Deletion of all insignificant variables with the exception of H and HI from the equation produces negligible changes in the remaining coefficients and their standard errors. Finally, on the basis of comparisons between the log of the likelihood function, 1, equation 1 better fits the data.

The quantitative importance of the statistically significant variables is best understood through the total effects of relevant changes in those variables on the probability of death, holding all other variables at their sample means. Such results are reported in Table II.l9 A change in BA from 0 to 10 (sober to legally intoxicated in most states) increases the probability of a fatality dramatically from .0207 to .0853 or from .0233 to .1131 depending on which equation is employed. In the same vain, an increase in the relevant crash speed from 40 to 60 mph increases the probability from .0708 to .3632 or from .0446 to .1230.

Table II - Total Effects On P(D = 1X)

Eq. 1

Eq. 2

All

X' = X'

.0228

.0262

BA

BA = 0

.0207

.0233

.0646

.0898

BA = 10

.0853

.1131

K

M = 5.01a

.0091

.0166

V = 0 mph

.0071

.0051

M = 5.01

.0162

.0217

V = 20 mph

.0546

.0229

M = 5.01

.0708

.0446

V = 40 mph

.2924

.0784

M = 5.01

.3632

.1230

V = 60 mph

aThe average weight and mass are respectively 161.19 and 5.01.

These results clearly establish that:

Crash speed and the blood alcohol level of the rider are the most important determinants of fatalities, while helmets are shown to have no statistically significant effect on the Probability of survival.

B. Head Injury Severity Model

Parameter estimates associated with the HIS model are reported in Table III. As in the previous model, the statistically most significant determinants of the severity of head injuries are the rider's kinetic energy and blood alcohol level. In sharp contrast to the previous model, methods for the reduction of the gravity of head injuries exist. The most effective one is the energy absorbing capability of the helmet. The statistical significance of the H variable and insignificance of the interaction term (HI) imply that not only do helmets reduce head injuries, but they do so at almost all realistic impact speeds to the helmet.20 For example in equation 3 at the average impact speed of 10.13 mph to riders experiencing an impact to the helmet, MS is reduced by 12.68. Other deterrents to head injuries include execution of the proper evasive action and rider experience. A rider with the average level of road experience receives a 2.99 reduction in HS while the reduction for a properly executed evasive action is 5.31. Finally, as in the fatality model, equation 3 better fits the data.

C. Neck Injury Severity Model

The results associated with the NIS model are reported in Table IV. The inclusion of the HW variable in the equations results in four variants of the model. As in the previous models K and BA are important determinants of injury severity, but in addition we find that:

Past a critical impact velocity to the helmet, measured by the normal component of velocity, helmet use has a statistically significant effect which exacerbates the severity of neck injuries.

Using the point estimates in equations 5-8 and the average weight of the helmet (2.70), estimates of this critical impact speed are around 13 mph. Beyond this realistically attained critical speed the energy absorbing ability of the helmet which is capable of reducing the extension- flexsion response of the neck to head impacts are surpassed. Under these circumstances, the inertial and post-impact response of the neck are intensified due to the added mass of the helmet and neck injuries result. An impact to the head whose normal component of velocity is 20 mph will increase the severity of neck injuries by around 10. Equations 7 and 8 also reveal that marginal increases in helmet weight do not have a statistically significant effect on the severity of neck injuries. This finding along with the acceptance of the zero constraints in equations 5 and 6 imply that it is the added mass of a helmet and not its specific weight that is responsible for exacerbating neck injuries.

Reductions in the severity of neck injuries are achieved through helmet use but only when impact velocities to the helmet are below the critical velocity. The proper execution of evasive action is also an effective deterrent to neck injuries. While the coefficient of EX in this model takes on an unexpected sign, the coefficient is not significantly different from zero. Finally, on the basis of likelihood comparisons, equation 5 better fits the data.

The most important finding generated by the HIS and NIS models is that:

A tradeoff between head and neck injuries confronts a potential helmet user.

Past a critical impact speed to the helmet, which is likely to occur in real life accident situations, helmet use reduces the severity of head injuries at the expense of increasing the severity of neck injuries. We now consider the qualitative nature of this tradeoff to discern if a helmet user forgoes either severe or minor head injuries in order to incur either severe or minor neck injuries.

D. The Nature of the Tradeoff

To gain insight into the nature of the head-neck injury tradeoff associated with helmet use, we specify and estimate two probit equations. The first considers the determinants of the

probability that a rider's most severe head injury is either critical or fatal (AIS > 5), while the second analogously considers a rider's most severe neck injury. In each respective case the vector of independent variables is the same as in the HIS and NIS models. We thus define HD = 1 if AISMH> 5 and HD = 0 if 0 < AISMH < 5, where the subscript MH refers to the rider's most severe head injury. Analogously, ND = 1 if AISMN> 5 and ND = 0 if 0 < AISMN < 5.21 Given that HD and ND are conditional on the occurrence of an accident, the sample size is the same as in the previous models. The estimates for these basic equations are reported in Table V.22

These results indicate that the only statistically significant determinants of the probability that an individual's most severe head or neck injury will be severe (critical or fatal) is the rider's blood alcohol level and kinetic energy which is dominated by the crash speed. With respect to helmets, this finding implies that both helmeted and non-helmeted riders are equally likely to-have their most severe head and neck injuries classified as severe or minor. This further suggests that, ceteris paribus, an individual who decides to wear a helmet and who experiences an impact velocity to the head greater than the critical level may forego either severe or minor head injuries and incur either a severe or minor neck injury; all forms of the tradeoff are equally likely to occur.

VI. Conclusions and Policy Implications

From our empirical results we conclude that helmet use has no statistically significant effect on the probability of a motorcycle fatality and that helmet users face a tradeoff between reductions in the severity of head injuries and increases in the severity of neck injuries. It is also shown that all possible combinations of the intensity of this tradeoff are equally likely to occur. In addition, it is found that the major determinants of injury and death are speed and blood alcohol level.

If a major concern of policy makers is the prevention of fatalities, our results imply that helmet legislation may not be effective in achieving that objective. Alternatively if the - overall costs to society in the form of health care costs and lost productive output are at issue, our results imply that existing cost-benefit analyzes which fail to consider the injury tradeoff are inappropriate for policy guidance.23 Until studies are adequately designed and completed, the passage of helmet use laws which may seriously jeopardize the health and earning capacities of an individual is not a viable policy option. Even in the event that cost-benefit studies show a net benefit to society from helmet legislation, the existence of externalities and high marginal disutilities associated with helmet use for all or a subset of motorcyclists may imply a net cost to the individual and thus raise questions about the redistribution of income resulting from helmet legislation.24 Furthermore, alterations in driving behavior in response to mandatory helmet use laws, predicted by the theories of risk compensation and risk homeostasis, may dissipate the net benefits to society from regulation.25

Under these circumstances mandatory helmet use laws cannot be considered as an effective method to eradicate the slaughter and maiming of individuals involved in motorcycle accidents. A more viable policy approach would be two pronged. On one hand, policy must address the causes of motorcycle accidents. On the other hand, since all accidents are not preventable, policy must consider the major determinants of death and injury and effective methods for their reduction.

Although our empirical results do not shed light on the causes of accidents, other evidence leads us to suggest the following policies: (1) the education of the general driving public about the coexistence of heterogeneous road users; (2) education of a younger and more inexperienced population of motorcyclists on the issues of accident avoidance and the proper use of all too often overpowered machines; and (3) stricter enforcement of drunk driving laws, an increase in the legal drinking age, and alcohol awareness programs to reduce the accident rate.

With respect to the second type of policy, our results show that the major determinants of death and injury are speed and alcohol consumption. Policies aimed at the former problem range from stricter enforcement of speed limits to horsepower restrictions on the vehicle population.26 In the latter case policy options are the same as those mentioned above. Finally, a viable alternative to helmets as a means for reducing the severity of head injuries exists. Mandatory driver training and education programs which emphasize the proper execution of evasive action in accident situations can effectively serve this purpose.